OP, feel free to ignore, but my recommendations would be…
I would suggest reading this: Shelter Scotland – Eviction before the end of your tenancy
And this: Shelter Scotland – Grounds for eviction for assured and short assured tenants
Basically, you’re legally entitled to evict your tenant before the end of their lease using ground #1 “Landlord wants property to be own home or the property was previously their own home“. To do this you must go through the proper legal process, as outlined in the first Shelter link I gave. Your tenant also has the legal right to defend themselves against eviction in court.
So I believe your agents are correct; they can serve notice to quit at the end of the tenancy, but you would have to wait. If you want in sooner, you need to serve an eviction notice.
I would think the best thing to do is contact the tenant directly and have a good chat with her. Going through your agent can result in mixed/wrong messages, even with best intentions. Explain your situation and the route you might have to go down, and whether she would be likely to comply or fight. Give her time to think about it and get back to you. If she’s adamant that she will fight it in court, you may decide it’s not worth the hassle. But unless she is deemed vulnerable, I would think that you have reasonable grounds for repossession if it went that far.
Anyway, you should contact either Shelter (0808 800 4444) or Landlord Accreditation Scotland (0131 553 2211). Both will give you much better advice than here.